Geodetic and Control Surveying: Datums, Projections, and Adjustment
Reference surfaces
Horizontal positions sit on a datum (NAD83, with realizations and epochs); heights relate to the ellipsoid or the geoid. Ellipsoid height h, orthometric height H, and geoid separation N satisfy H = h - N (careful with sign conventions). A geoid model such as GEOID18 supplies N. Trap: treating an RTK ellipsoid height as an elevation, or mixing data from different datum realizations without transformation.
Projections and grid
State Plane coordinates use Lambert conformal conic or transverse Mercator zones; UTM uses six-degree transverse Mercator zones with a central meridian scale factor of 0.9996. Grid distance relates to ground distance through scale factor and elevation factor: elevation factor = R / (R + h), combined factor = scale x elevation factor, and ground distance = grid distance / combined factor. Grid azimuth differs from geodetic azimuth by convergence.
Control, GNSS, and adjustment
Control networks use triangulation, trilateration, traversing, leveling, and GNSS static or RTK/RTN methods. Loop misclosure is tested against project tolerance. Least-squares adjustment yields residuals, reference variance, and error ellipses; a large standard error of unit weight signals a weighting or blunder problem, not merely a tight network. Check monument stability and repeatability, and document epochs.
Worked example
Scale factor 0.99996, elevation factor 0.99990; combined factor = 0.99986. A grid distance of 1,000.00 ft corresponds to ground distance 1,000.00 / 0.99986 = 1,000.14 ft.